In [114]:
!pip install numpy pandas matplotlib seaborn
!pip install scikit-learn
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import re
import numpy as np
from scipy.stats import zscore
from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error

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In [59]:
# Introduction
# Our dataset comes from Kaggle, and can be found at here: https://www.kaggle.com/datasets/sudhanvahg/wind-turbine-power-generation-forecasting
# This dataset includes data on the hourly meteorological data along with power output measurements from wind turbines collected between Jan 2013 
# and December 2016. The data is split into two portions, a train set and a test set. The included variables are temperature, relative humidity,
# windspeed at different altitudes (2m,10m, 100m), as well as dew point, and wind direction for these altitudes as well. There are 140160 entries
# in our train dataset, and 35040 entries in our test dataset. There are no null values.

# Let's also discuss our goal for the project a bit. My intentions are to create a model that can predict the power generated by turbines
# as accurately as possible, with our model producing an r^2 value of above .7 at the least when comparing test values to predicted values.
In [60]:
# What is regression?
# Linear regression is a method used to model relationships between data, and uses known values to predict unknown target values. It attempts to fit
# lines to our data, and then picks the best line to then predict target values based off of that line. One of the ways to measure how good of a model 
# we have is the R-squared value of a model. The R-squared value is a ratio of the residual sum of squared divided by the total sum of squares.
In [61]:
wt_train_df_raw = pd.read_csv("train.csv");
wt_test_df_raw = pd.read_csv("test.csv");
In [62]:
wt_train_df_raw.describe()
Out[62]:
Unnamed: 0 Location Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m Power
count 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000 140160.000000
mean 17519.500000 2.500000 45.912162 70.420512 35.867228 4.352948 6.924278 200.684417 200.649010 8.027673 0.312437
std 10115.212797 1.118038 21.930554 17.000203 20.979720 2.027149 3.056636 100.079917 101.105919 3.626641 0.253774
min 0.000000 1.000000 -31.420400 8.664205 -36.627405 0.165389 0.007799 0.051683 -0.942685 0.436515 -0.000004
25% 8759.750000 1.750000 29.579600 57.664205 21.172595 2.815389 4.747799 128.051683 127.057315 5.236515 0.099696
50% 17519.500000 2.500000 45.879600 72.664205 35.672595 4.055389 6.717799 211.051683 211.057315 7.636515 0.246896
75% 26279.250000 3.250000 64.579600 84.664205 53.872595 5.575389 8.847799 287.051683 289.057315 10.236515 0.486396
max 35039.000000 4.000000 94.479600 99.664205 78.272595 18.695389 24.597799 359.051683 359.057315 28.936515 0.988796
In [63]:
wt_test_df_raw.describe()
Out[63]:
Unnamed: 0 Location Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m
count 35040.000000 35040.00000 35040.000000 35040.000000 35040.000000 35040.000000 35040.000000 35040.000000 35040.000000 35040.000000
mean 39419.500000 2.50000 48.529326 67.415432 36.975266 4.203348 6.738558 200.467978 200.385882 7.762908
std 2528.830248 1.11805 22.215776 18.380048 20.722451 1.949184 2.988170 97.856886 98.978351 3.572855
min 35040.000000 1.00000 -26.920400 15.664205 -32.727405 0.165389 0.107799 0.051683 -0.942685 0.436515
25% 37229.750000 1.75000 31.879600 53.664205 22.672595 2.725389 4.587799 133.051683 132.057315 5.036515
50% 39419.500000 2.50000 49.679600 68.664205 36.372595 3.885389 6.557799 205.051683 205.057315 7.336515
75% 41609.250000 3.25000 66.879600 82.664205 55.072595 5.405389 8.637799 284.051683 286.057315 10.036515
max 43799.000000 4.00000 101.479600 99.664205 75.272595 15.535389 22.847799 359.051683 359.057315 29.136515
In [64]:
wt_train_df_raw.isna().sum()
Out[64]:
Unnamed: 0    0
Time          0
Location      0
Temp_2m       0
RelHum_2m     0
DP_2m         0
WS_10m        0
WS_100m       0
WD_10m        0
WD_100m       0
WG_10m        0
Power         0
dtype: int64
In [65]:
wt_test_df_raw.isna().sum()
Out[65]:
Unnamed: 0    0
Time          0
Location      0
Temp_2m       0
RelHum_2m     0
DP_2m         0
WS_10m        0
WS_100m       0
WD_10m        0
WD_100m       0
WG_10m        0
dtype: int64
In [66]:
wt_train_df_raw.head()
Out[66]:
Unnamed: 0 Time Location Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m Power
0 0 02-01-2013 00:00 1 28.2796 84.664205 24.072595 1.605389 1.267799 145.051683 161.057315 1.336515 0.163496
1 1 02-01-2013 01:00 1 28.1796 85.664205 24.272595 2.225389 3.997799 150.051683 157.057315 4.336515 0.142396
2 2 02-01-2013 02:00 1 26.5796 90.664205 24.072595 1.465389 2.787799 147.051683 149.057315 3.136515 0.121396
3 3 02-01-2013 03:00 1 27.1796 87.664205 23.872595 1.465389 2.697799 57.051683 104.057315 1.536515 0.100296
4 4 02-01-2013 04:00 1 27.0796 87.664205 23.672595 2.635389 4.437799 57.051683 83.057315 3.936515 0.079296
In [67]:
# Preprocessing for our Models
# So far, The first thing I see we can drop is the "unnamed: 0" column, this appears to just be an index column for our data, which we won't need. 
# We'll also be dropping the location of each, since we really don't have any information on where exactly these locations are.
# We'll be dropping the time data as well for now. We'll likely revisit this later by potentially pulling out the time of day as well as 
# splitting our entries into the 4 seasons.
# In addition to this, there may be some outliers in our dataset that we can get rid of to look at more accurate data, since we have such a 
# large dataset it would be good to remove outliers as to not skew our results. We can check our graphs in a pairplot just to see if there are 
# potentially any outliers.
In [68]:
wt_test_df = wt_test_df_raw.drop('Unnamed: 0', axis=1)
wt_test_df = wt_test_df.drop('Location', axis = 1)
wt_test_df = wt_test_df.drop('Time', axis = 1)
wt_test_df.head()
Out[68]:
Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m
0 19.6796 89.664205 17.072595 1.085389 0.867799 192.051683 233.057315 1.636515
1 19.1796 90.664205 16.672595 1.665389 1.907799 183.051683 197.057315 2.736515
2 19.5796 88.664205 16.672595 1.845389 2.867799 162.051683 167.057315 2.736515
3 20.3796 85.664205 16.572595 2.325389 3.987799 166.051683 161.057315 2.936515
4 21.0796 82.664205 16.572595 2.265389 4.047799 182.051683 170.057315 3.136515
In [69]:
wt_train_df = wt_train_df_raw.drop('Unnamed: 0', axis=1)
wt_train_df = wt_train_df.drop('Location', axis = 1)
wt_train_df = wt_train_df.drop('Time', axis = 1)
wt_train_df.head()
Out[69]:
Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m Power
0 28.2796 84.664205 24.072595 1.605389 1.267799 145.051683 161.057315 1.336515 0.163496
1 28.1796 85.664205 24.272595 2.225389 3.997799 150.051683 157.057315 4.336515 0.142396
2 26.5796 90.664205 24.072595 1.465389 2.787799 147.051683 149.057315 3.136515 0.121396
3 27.1796 87.664205 23.872595 1.465389 2.697799 57.051683 104.057315 1.536515 0.100296
4 27.0796 87.664205 23.672595 2.635389 4.437799 57.051683 83.057315 3.936515 0.079296
In [70]:
# Data Understanding/Visualization
sns.pairplot(wt_train_df)
Out[70]:
<seaborn.axisgrid.PairGrid at 0x2d422de91f0>
No description has been provided for this image
In [71]:
# based on the above pairplot, it does look like we have a few outliers here and there, especially in our windspeed graphs, so lets figure out more 
# about how to deal with outliers. We can get the z-score from our data, which is a measurement that describes a values relationship relative to 
# our data's mean (average). It is measured in standard deviations from the mean, so a higher z-score is more indicative of the value being an outlier.
# we'll use this to remove values that are more than 3 standard deviations from the mean. 3 standard deviations should include about 99.7% of our data,
# so this is a great way for us to omit our outliers.
In [72]:
# To explain what we're doing below, we take the absolute value of each z-score, and we're removing those entries which have values that have z-scores
# that are more than 3 standard deviations from the mean of our data in either direction (below or above).
columns_to_score = ['Temp_2m','RelHum_2m','DP_2m','WS_10m','WS_100m','WD_10m','WD_100m','WG_10m','Power']
z_scores = np.abs(wt_train_df[columns_to_score].apply(zscore))
filtered_rows = (z_scores < 3).all(axis=1)
wt_train_df_flt = wt_train_df[filtered_rows]
In [73]:
wt_train_df_flt.describe()
Out[73]:
Temp_2m RelHum_2m DP_2m WS_10m WS_100m WD_10m WD_100m WG_10m Power
count 138519.000000 138519.000000 138519.000000 138519.000000 138519.000000 138519.000000 138519.000000 138519.000000 138519.000000
mean 46.117744 70.478512 36.092496 4.282069 6.828647 200.037186 199.993453 7.910036 0.309281
std 21.803271 16.955317 20.827574 1.903810 2.911459 100.063676 101.088483 3.446334 0.251757
min -19.820400 19.664205 -26.927405 0.165389 0.007799 0.051683 -0.942685 0.436515 -0.000004
25% 29.679600 57.664205 21.272595 2.805389 4.717799 127.051683 126.057315 5.236515 0.098696
50% 46.279600 72.664205 35.872595 4.015389 6.677799 210.051683 210.057315 7.536515 0.244196
75% 64.679600 84.664205 54.072595 5.515389 8.767799 287.051683 288.057315 10.236515 0.480096
max 94.479600 99.664205 78.272595 10.425389 16.067799 359.051683 359.057315 18.836515 0.985896
In [74]:
# With this, we've cut our dataframe down from 140160 entries to 138519 entries, meaning we've removed about 1641 entries that were outliers
# from our data. Awesome!

# Now let's gauge the relationships between our values, to do this, we'll be using a correlation matrix.
In [75]:
sns.heatmap(wt_train_df_flt.corr(), annot = True)
plt.show()
No description has been provided for this image
In [76]:
# Our data with the highest correlation to our power outputs are the wind speeds at 10m and 100m from the ground,
# as well as the wind gusts at 10m above the ground.
In [77]:
# Model 1
In [81]:
# At a glance, our provided test set doesn't include any values for the power generated, which doesn't help us much in creating our model. So we'll need
# to split and use our train data set to create our model.
X = wt_train_df_flt.drop(labels = 'Power', axis = 1)
y = wt_train_df_flt['Power']
In [90]:
# i'll split my train data into training data into train and test sets
# wt_train, wt_test = train_test_split(wt_train_df_model, test_size = .2, random_state = 42)
# target_train,target_test = train_test_split(wt_train_df_target, test_size = .2, random_state = 42)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = .2, random_state = 42)
print("X_train", X_train.shape)
print("X_test", X_test.shape)
print("y_train", y_train.shape)
print("y_test", y_test.shape)

X_train (110815, 8)
X_test (27704, 8)
y_train (110815,)
y_test (27704,)
In [92]:
# Lets do a linear regression model on our train and test sets now!
wt_linear_model = linear_model.LinearRegression()
wt_linear_model.fit(X_train, y_train)
Out[92]:
LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
LinearRegression()
In [93]:
# lets see how well our training data performs
y_pred = wt_linear_model.predict(X_train)
In [95]:
wt_linear_model.score(X_train, y_train)
Out[95]:
0.4754723450463729
In [94]:
# Currently, our model has an R-Squared value of about .48, which isn't great. Typically, the closer a value is to 1 the better, and our score right
# now isn't looking so hot. We might remedy this by removing some of those columns that we saw don't have a good correlation to our power generated
# on our correlation matrix, such as temperature and dew point at 2 meters.
In [127]:
np.sqrt(mean_squared_error(y_train, y_pred))
Out[127]:
0.18241379165429816
In [ ]:
# However, RMSE values closer to 0 are great, and as long as I didn't mess something up, our RMSE value is actually pretty solid. Our model might
# actually be redeemable!